Myomodulin increases Ih and inhibits the NA/K pump to modulate bursting in leech heart interneurons

Ih Block Reveals Separation of Timescales in Pyloric Rhythm Response to Temperature Changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the contribution of the hyperpolarization-activated inward current (Ih) to frequency and phase in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis as temperature was altered from 11°C to 21°C. Under control conditions, the frequency of the rhythm increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. When we blocked Ih with cesium (Cs+) PD offset, LP onset, and LP offset were all phase advanced in Cs+ at 11°C, and the latter two further advanced as temperature increased. In Cs+ the steady state increase in pyloric frequency with temperature diminished and the Q10 of the pyloric frequency dropped from ~1.75 to ~1.35. Unexpectedly in Cs+, the frequency displayed non-monotonic dynamics during temperature transitions; the frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic "jag". Interestingly, these jags were still present during temperature transitions in Cs+ when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that Ih plays an important role in the ability of this circuit to produce smooth transitory responses and persistent frequency increases by different mechanisms during temperature fluctuations.

Dynamics of antiphase bursting modulated by the inhibitory synaptic and hyperpolarization-activated cation currents

Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (Isyn), especially in the presence of the hyperpolarization-activated cation current (Ih). In the present paper, the dynamics of antiphase bursting modulated by the Ih and Isyn is studied in three aspects with a theoretical model. Firstly, the Isyn and the slow Ih with strong strength are the identified to be the necessary conditions for the antiphase bursting. The dependence of the antiphase bursting on the two currents is different for low (escape mode) and high (release mode) threshold voltages (Vth) of the inhibitory synapse. Secondly, more detailed co-regulations of the two currents to induce opposite changes of the bursting period are obtained. For the escape mode, increase of the Ih induces elevated membrane potential of the silence inhibited by a strong Isyn and shortened silence duration to go beyond Vth, resulting in reduced bursting period. For the release mode, increase of the Ih induces elevated tough value of the former part of the burst modulated by a nearly zero Isyn and lengthen burst duration to fall below Vth, resulting in prolonged bursting period. Finally, the fast-slow dynamics of the antiphase bursting are acquired. Using one-and two-parameter bifurcations of the fast subsystem of a single neuron, the burst of the antiphase bursting is related to the stable limit cycle, and the silence modulated by a strong Isyn to the stable equilibrium to a certain extent. The Ih mainly modulates the dynamics within the burst and quiescent state. Furthermore, with the fast subsystem of the coupled neurons, the silence is associated with the unstable equilibrium point. The results present theoretical explanations to the changes in the bursting period and fast-slow dynamics of the antiphase bursting modulated by the Isyn and Ih, which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

Multiple intrinsic membrane properties are modulated in a switch from single- to dual-network activity

Neural network flexibility includes changes in neuronal participation between networks, such as the switching of neurons between single- and dual-network activity. We previously identified a neuron that is recruited to burst in time with an additional network via modulation of its intrinsic membrane properties, instead of being recruited synaptically into the second network. However, the modulated intrinsic properties were not determined. Here, we use small networks in the Jonah crab (Cancer borealis) stomatogastric nervous system (STNS) to examine modulation of intrinsic properties underlying neuropeptide (Gly1-SIFamide)-elicited neuronal switching. The lateral posterior gastric neuron (LPG) switches from exclusive participation in the fast pyloric (∼1 Hz) network, due to electrical coupling, to dual-network activity that includes periodic escapes from the fast rhythm via intrinsically generated oscillations at the slower gastric mill network frequency (∼0.1 Hz). We isolated LPG from both networks by pharmacology and hyperpolarizing current injection. Gly1-SIFamide increased LPG intrinsic excitability and rebound from inhibition and decreased spike frequency adaptation, which can all contribute to intrinsic bursting. Using ion substitution and channel blockers, we found that a hyperpolarization-activated current, a persistent sodium current, and calcium or calcium-related current(s) appear to be primary contributors to Gly1-SIFamide-elicited LPG intrinsic bursting. However, this intrinsic bursting was more sensitive to blocking currents when LPG received rhythmic electrical coupling input from the fast network than in the isolated condition. Overall, a switch from single- to dual-network activity can involve modulation of multiple intrinsic properties, while synaptic input from a second network can shape the contributions of these properties.NEW & NOTEWORTHY Neuropeptide-elicited intrinsic bursting was recently determined to switch a neuron from single- to dual-network participation. Here we identified multiple intrinsic properties modulated in the dual-network state and candidate ion channels underlying the intrinsic bursting. Bursting at the second network frequency was more sensitive to blocking currents in the dual-network state than when neurons were synaptically isolated from their home network. Thus, synaptic input can shape the contributions of modulated intrinsic properties underlying dual-network activity.

Contributions of h- and Na+/K+ Pump Currents to the Generation of Episodic and Continuous Rhythmic Activities

Developing spinal motor networks produce a diverse array of outputs, including episodic and continuous patterns of rhythmic activity. Variation in excitability state and neuromodulatory tone can facilitate transitions between episodic and continuous rhythms; however, the intrinsic mechanisms that govern these rhythms and their transitions are poorly understood. Here, we tested the capacity of a single central pattern generator (CPG) circuit with tunable properties to generate multiple outputs. To address this, we deployed a computational model composed of an inhibitory half-center oscillator (HCO). Following predictions of our computational model, we tested the contributions of key properties to the generation of an episodic rhythm produced by isolated spinal cords of the newborn mouse. The model recapitulates the diverse state-dependent rhythms evoked by dopamine. In the model, episodic bursting depended predominantly on the endogenous oscillatory properties of neurons, with Na⁺/K⁺ ATPase pump (I_Pump) and hyperpolarization-activated currents (I_h) playing key roles. Modulation of either I_Pump or I_h produced transitions between episodic and continuous rhythms and silence. As maximal activity of I_Pump decreased, the interepisode interval and period increased along with a reduction in episode duration. Decreasing maximal conductance of I_h decreased episode duration and increased interepisode interval. Pharmacological manipulations of I_h with ivabradine, and I_Pump with ouabain or monensin in isolated spinal cords produced findings consistent with the model. Our modeling and experimental results highlight key roles of I_h and I_Pump in producing episodic rhythms and provide insight into mechanisms that permit a single CPG to produce multiple patterns of rhythmicity.

Bimodal modulation of short-term motor memory via dynamic sodium pumps in a vertebrate spinal cord

Dynamic neuronal Na⁺/K⁺ pumps normally only respond to intense action potential firing owing to their low affinity for intracellular Na⁺. Recruitment of these Na⁺ pumps produces a post-activity ultraslow afterhyperpolarization (usAHP) up to ∼10 mV in amplitude and ∼60 s in duration, which influences neuronal properties and future network output. In spinal motor networks, the usAHP underlies short-term motor memory (STMM), reducing the intensity and duration of locomotor network output in a manner dependent on the interval between locomotor bouts. In contrast to tonically active Na⁺ pumps that help set and maintain the resting membrane potential, dynamic Na⁺ pumps are selectively antagonized by low concentrations of ouabain, which, we show, blocks both the usAHP and STMM. We examined whether dynamic Na⁺ pumps and STMM can be influenced by neuromodulators, focusing on 5-HT and nitric oxide. Bath-applied 5-HT alone had no significant effect on the usAHP or STMM. However, this is due to the simultaneous activation of two distinct 5-HT receptor subtypes (5-HT7 and 5-HT2a) that have opposing facilitatory and suppressive influences, respectively, on these two features of the locomotor system. Nitric oxide modulation exerts a potent inhibitory effect that can completely block the usAHP and erase STMM. Using selective blockers of 5-HT7 and 5-HT2a receptors and a nitric oxide scavenger, PTIO, we further provide evidence that the two modulators constitute an endogenous control system that determines how the spinal network self-regulates the intensity of locomotor output in light of recent past experience.

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Short-term memory in a spinal locomotor network is controlled by dynamic Na⁺ pumps

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Na⁺ pumps mediate an underlying ultraslow AHP modulated by 5-HT receptors and NO

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5-HT7Rs increase and 5-HT2aRs and NO decrease the usAHP and short-term motor memory

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Endogenous 5-HT and NO regulate the usAHP and short-term motor memory

Comodulation of h- and Na+/K+ Pump Currents Expands the Range of Functional Bursting in a Central Pattern Generator by Navigating between Dysfunctional Regimes

Central pattern generators (CPGs), specialized oscillatory neuronal networks controlling rhythmic motor behaviors such as breathing and locomotion, must adjust their patterns of activity to a variable environment and changing behavioral goals. Neuromodulation adjusts these patterns by orchestrating changes in multiple ionic currents. In the medicinal leech, the endogenous neuromodulator myomodulin speeds up the heartbeat CPG by reducing the electrogenic Na+/K+ pump current and increasing h-current in pairs of mutually inhibitory leech heart interneurons (HNs), which form half-center oscillators (HN HCOs). Here we investigate whether the comodulation of two currents could have advantages over a single current in the control of functional bursting patterns of a CPG. We use a conductance-based biophysical model of an HN HCO to explain the experimental effects of myomodulin. We demonstrate that, in the model, comodulation of the Na+/K+ pump current and h-current expands the range of functional bursting activity by avoiding transitions into nonfunctional regimes, such as asymmetric bursting and plateau-containing seizure-like activity. We validate the model by finding parameters that reproduce temporal bursting characteristics matching experimental recordings from HN HCOs under control, three different myomodulin concentrations, and Cs+ treated conditions. The matching cases are located along the border of an asymmetric regime away from the border with more dangerous seizure-like activity. We found a simple comodulation mechanism with an inverse relation between the pump and h-currents makes a good fit of the matching cases and comprises a general mechanism for the robust and flexible control of oscillatory neuronal networks.SIGNIFICANCE STATEMENT Rhythm-generating neuronal circuits adjust their oscillatory patterns to accommodate a changing environment through neuromodulation. In different species, chemical messengers participating in such processes may target two or more membrane currents. In medicinal leeches, the neuromodulator myomodulin speeds up the heartbeat central pattern generator by reducing Na+/K+ pump current and increasing h-current. In a computational model, we show that this comodulation expands the range of central pattern generator's functional activity by navigating the circuit between dysfunctional regimes resulting in a much wider range of cycle period. This control would not be attainable by modulating only one current, emphasizing the synergy of combined effects. Given the prevalence of h-current and Na+/K+ pump current in neurons, similar comodulation mechanisms may exist across species.

Immune Tolerance in Mytilus galloprovincialis Hemocytes After Repeated Contact With Vibrio splendidus

Mediterranean mussels (Mytilus galloprovincialis) are sessile filter feeders that live in close contact with numerous marine microorganisms. As is the case in all invertebrates, mussels lack an adaptive immune system, but they respond to pathogens, injuries or environmental stress in a very efficient manner. However, it is not known if they are able to modify their immune response when they reencounter the same pathogen. In this work, we studied the transcriptomic response of mussel hemocytes before and after two consecutive sublethal challenges with Vibrio splendidus. The first exposure significantly regulated genes related to inflammation, migration and response to bacteria. However, after the second exposure, the differentially expressed genes were related to the control and inhibition of ROS production and the resolution of the inflammatory response. Our results also show that the second injection with V. splendidus led to changes at the transcriptional (control of the expression of pro-inflammatory transcripts), cellular (shift in the hemocyte population distribution), and functional levels (inhibition of ROS production). These results suggest that a modified immune response after the second challenge allowed the mussels to tolerate rather than fight the infection, which minimized tissue damage.

Control of Xenopus Tadpole Locomotion via Selective Expression of Ih in Excitatory Interneurons

Locomotion relies on the coordinated activity of rhythmic neurons in the hindbrain and spinal cord and depends critically on the intrinsic properties of excitatory interneurons. Therefore, understanding how ion channels sculpt the properties of these interneurons, and the consequences for circuit function and behavior, is an important task. The hyperpolarization-activated cation current, Ih, is known to play important roles in shaping neuronal properties and for rhythm generation in many neuronal networks. We show in stage 42 Xenopus laevis frog tadpoles that Ih is strongly expressed only in excitatory descending interneurons (dINs), an important ipsilaterally projecting population that drives swimming activity. The voltage-dependent HCN channel blocker ZD7288 completely abolished a prominent depolarizing sag potential in response to hyperpolarization, the hallmark of Ih, and hyperpolarized dINs. ZD7288 also affected dIN post-inhibitory rebound firing, upon which locomotor rhythm generation relies, and disrupted locomotor output. Block of Ih also unmasked an activity-dependent ultraslow afterhyperpolarization (usAHP) in dINs following swimming, mediated by a dynamic Na/K pump current. This usAHP, unmasked in dINs by ZD7288, resulted in suprathreshold stimuli failing to evoke swimming at short inter-swim intervals, indicating an important role for Ih in maintaining swim generation capacity and in setting the post-swim refractory period of the network. Collectively, our data suggest that the selective expression of Ih in dINs determines specific dIN properties that are important for rhythm generation and counteracts an activity-dependent usAHP to ensure that dINs can maintain coordinated swimming over a wide range of inter-swim intervals.

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Ih is strongly expressed in Xenopus locomotor-rhythm-generating dIN interneurons

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Ih is active at rest in dINs, contributing to their distinct electrical properties

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dINs normally lack a Na pump-dependent ultra-slow afterhyperpolarization (usAHP)

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Ih counterbalances dIN usAHPs to preserve tadpole rhythm generating capacity

Na+/K+-pump and neurotransmitter membrane receptors

Na⁺/K⁺-pump is an electrogenic transmembrane ATPase located in the outer plasma membrane of cells. The Na⁺/K⁺-ATPase pumps 3 sodium ions out of cells while pumping 2 potassium ions into cells. Both cations move against their concentration gradients. This enzyme's electrogenic nature means that it has a chronic role in stabilizing the resting membrane potential of the cell, in regulating the cell volume and in the signal transduction of the cell. This review will mainly consider the role of the Na⁺/K⁺-pump in neurons, with an emphasis on its role in modulating neurotransmitter receptor. Most of the literature on the modulation of neurotransmitter receptors refers to the situation in the mammalian nervous system, but the position is likely to be similar in most, if not all, invertebrate nervous systems.

Propensity for Bistability of Bursting and Silence in the Leech Heart Interneuron

The coexistence of neuronal activity regimes has been reported under normal and pathological conditions. Such multistability could enhance the flexibility of the nervous system and has many implications for motor control, memory, and decision making. Multistability is commonly promoted by neuromodulation targeting specific membrane ionic currents. Here, we investigated how modulation of different ionic currents could affect the neuronal propensity for bistability. We considered a leech heart interneuron model. It exhibits bistability of bursting and silence in a narrow range of the leak current parameters, conductance (g_leak) and reversal potential (E_leak). We assessed the propensity for bistability of the model by using bifurcation diagrams. On the diagram (g_leak, E_leak), we mapped bursting and silent regimes. For the canonical value of E_leak we determined the range of g_leak which supported the bistability. We use this range as an index of propensity for bistability. We investigated how this index was affected by alterations of ionic currents. We systematically changed their conductances, one at a time, and built corresponding bifurcation diagrams in parameter planes of the maximal conductance of a given current and the leak conductance. We found that conductance of only one current substantially affected the index of propensity; the increase of the maximal conductance of the hyperpolarization-activated cationic current increased the propensity index. The second conductance with the strongest effect was the conductance of the low-threshold fast Ca²⁺ current; its reduction increased the propensity index although the effect was about two times smaller in magnitude. Analyzing the model with both changes applied simultaneously, we found that the diagram (g_leak, E_leak) showed a progressively expanded area of bistability of bursting and silence.

Sodium Pumps Mediate Activity-Dependent Changes in Mammalian Motor Networks

Ubiquitously expressed sodium pumps are best known for maintaining the ionic gradients and resting membrane potential required for generating action potentials. However, activity- and state-dependent changes in pump activity can also influence neuronal firing and regulate rhythmic network output. Here we demonstrate that changes in sodium pump activity regulate locomotor networks in the spinal cord of neonatal mice. The sodium pump inhibitor, ouabain, increased the frequency and decreased the amplitude of drug-induced locomotor bursting, effects that were dependent on the presence of the neuromodulator dopamine. Conversely, activating the pump with the sodium ionophore monensin decreased burst frequency. When more "natural" locomotor output was evoked using dorsal-root stimulation, ouabain increased burst frequency and extended locomotor episode duration, whereas monensin slowed and shortened episodes. Decreasing the time between dorsal-root stimulation, and therefore interepisode interval, also shortened and slowed activity, suggesting that pump activity encodes information about past network output and contributes to feedforward control of subsequent locomotor bouts. Using whole-cell patch-clamp recordings from spinal motoneurons and interneurons, we describe a long-duration (∼60 s), activity-dependent, TTX- and ouabain-sensitive, hyperpolarization (∼5 mV), which is mediated by spike-dependent increases in pump activity. The duration of this dynamic pump potential is enhanced by dopamine. Our results therefore reveal sodium pumps as dynamic regulators of mammalian spinal motor networks that can also be affected by neuromodulatory systems. Given the involvement of sodium pumps in movement disorders, such as amyotrophic lateral sclerosis and rapid-onset dystonia parkinsonism, knowledge of their contribution to motor network regulation also has considerable clinical importance.

SIGNIFICANCE STATEMENT

The sodium pump is ubiquitously expressed and responsible for at least half of total brain energy consumption. The pumps maintain ionic gradients and the resting membrane potential of neurons, but increasing evidence suggests that activity- and state-dependent changes in pump activity also influence neuronal firing. Here we demonstrate that changes in sodium pump activity regulate locomotor output in the spinal cord of neonatal mice. We describe a sodium pump-mediated afterhyperpolarization in spinal neurons, mediated by spike-dependent increases in pump activity, which is affected by dopamine. Understanding how sodium pumps contribute to network regulation and are targeted by neuromodulators, including dopamine, has clinical relevance due to the role of the sodium pump in diseases, including amyotrophic lateral sclerosis, parkinsonism, epilepsy, and hemiplegic migraine.

Sodium pump regulation of locomotor control circuits

Sodium pumps are ubiquitously expressed membrane proteins that extrude three Na⁺ ions in exchange for two K⁺ ions, using ATP as an energy source. Recent studies have illuminated additional, dynamic roles for sodium pumps in regulating the excitability of neuronal networks in an activity-dependent fashion. We review their role in a novel form of short-term memory within rhythmic locomotor networks. The data we review derives mainly from recent studies on Xenopus tadpoles and neonatal mice. The role and underlying mechanisms of pump action broadly match previously published data from an invertebrate, the Drosophila larva. We therefore propose a highly conserved mechanism by which sodium pump activity increases following a bout of locomotion. This results in an ultraslow afterhyperpolarization (usAHP) of the membrane potential that lasts around 1 min, but which only occurs in around half the network neurons. This usAHP in turn alters network excitability so that network output is reduced in a locomotor interval-dependent manner. The pumps therefore confer on spinal locomotor networks a temporary memory trace of recent network performance.

Amplitude-Modulated Bursting: A Novel Class of Bursting Rhythms

We report on the discovery of a novel class of bursting rhythms, called amplitude-modulated bursting (AMB), in a model for intracellular calcium dynamics. We find that these rhythms are robust and exist on open parameter sets. We develop a new mathematical framework with broad applicability to detect, classify, and rigorously analyze AMB. Here we illustrate this framework in the context of AMB in a model of intracellular calcium dynamics. In the process, we discover a novel family of singularities, called toral folded singularities, which are the organizing centers for the amplitude modulation and exist generically in slow-fast systems with two or more slow variables.

Na(+)/K(+) pump interacts with the h-current to control bursting activity in central pattern generator neurons of leeches

The dynamics of different ionic currents shape the bursting activity of neurons and networks that control motor output. Despite being ubiquitous in all animal cells, the contribution of the Na(+)/K(+) pump current to such bursting activity has not been well studied. We used monensin, a Na(+)/H(+) antiporter, to examine the role of the pump on the bursting activity of oscillator heart interneurons in leeches. When we stimulated the pump with monensin, the period of these neurons decreased significantly, an effect that was prevented or reversed when the h-current was blocked by Cs(+). The decreased period could also occur if the pump was inhibited with strophanthidin or K(+)-free saline. Our monensin results were reproduced in model, which explains the pump's contributions to bursting activity based on Na(+) dynamics. Our results indicate that a dynamically oscillating pump current that interacts with the h-current can regulate the bursting activity of neurons and networks.

The neural control of heartbeat in invertebrates

The neurogenic heartbeat of certain invertebrates has long been studied both as a way of understanding how automatic functions are regulated and for how neuronal networks generate the inherent rhythmic activity that controls and coordinates this vital function. This review focuses on the heartbeat of decapod crustaceans and hirudinid leeches, which remain important experimental systems for the exploration of central pattern generator networks, their properties, network and cellular mechanisms, modulation, and how animal-to-animal variation in neuronal and network properties are managed to produce functional output.

Neuromodulation of circuits with variable parameters: single neurons and small circuits reveal principles of state-dependent and robust neuromodulation

Neuromodulation underlies many behavioral states and has been extensively studied in small circuits. This has allowed the systematic exploration of how neuromodulatory substances and the neurons that release them can influence circuit function. The physiological state of a network and its level of activity can have profound effects on how the modulators act, a phenomenon known as state dependence. We provide insights from experiments and computational work that show how state dependence can arise and the consequences it can have for cellular and circuit function. These observations pose a general unsolved question that is relevant to all nervous systems: How is robust modulation achieved in spite of animal-to-animal variability and degenerate, nonlinear mechanisms for the production of neuronal and network activity?

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators.

The neuropeptide complement of the marine annelid Platynereis dumerilii

Background

The marine annelid Platynereis dumerilii is emerging as a powerful lophotrochozoan experimental model for evolutionary developmental biology (evo-devo) and neurobiology. Recent studies revealed the presence of conserved neuropeptidergic signaling in Platynereis, including vasotocin/neurophysin, myoinhibitory peptide and opioid peptidergic systems. Despite these advances, comprehensive peptidome resources have yet to be reported.

Results

The present work describes the neuropeptidome of Platynereis. We established a large transcriptome resource, consisting of stage-specific next-generation sequencing datasets and 77,419 expressed sequence tags. Using this information and a combination of bioinformatic searches and mass spectrometry analyses, we increased the known proneuropeptide (pNP) complement of Platynereis to 98. Based on sequence homology to metazoan pNPs, Platynereis pNPs were grouped into ancient eumetazoan, bilaterian, protostome, lophotrochozoan, and annelid families, and pNPs only found in Platynereis. Compared to the planarian Schmidtea mediterranea, the only other lophotrochozoan with a large-scale pNP resource, Platynereis has a remarkably full complement of conserved pNPs, with 53 pNPs belonging to ancient eumetazoan or bilaterian families. Our comprehensive search strategy, combined with analyses of sequence conservation, also allowed us to define several novel lophotrochozoan and annelid pNP families. The stage-specific transcriptome datasets also allowed us to map changes in pNP expression throughout the Platynereis life cycle.

Conclusion

The large repertoire of conserved pNPs in Platynereis highlights the usefulness of annelids in comparative neuroendocrinology. This work establishes a reference dataset for comparative peptidomics in lophotrochozoans and provides the basis for future studies of Platynereis peptidergic signaling.

Dopamine modulates auditory responses in the inferior colliculus in a heterogeneous manner

Perception of complex sounds such as speech is affected by a variety of factors, including attention, expectation of reward, physiological state, and/or disorders, yet the mechanisms underlying this modulation are not well understood. Although dopamine is commonly studied for its role in reward-based learning and in disorders, multiple lines of evidence suggest that dopamine is also involved in modulating auditory processing. In this study, we examined the effects of dopamine application on neuronal response properties in the inferior colliculus (IC) of awake mice. Because the IC contains dopamine receptors and nerve terminals immunoreactive for tyrosine hydroxylase, we predicted that dopamine would modulate auditory responses in the IC. We recorded single-unit responses before, during, and after the iontophoretic application of dopamine using piggyback electrodes. We examined the effects of dopamine on firing rate, timing, and probability of bursting. We found that application of dopamine affected neural responses in a heterogeneous manner. In more than 80 % of the neurons, dopamine either increased (32 %) or decreased (50 %) firing rate, and the effects were similar on spontaneous and sound-evoked activity. Dopamine also either increased or decreased first spike latency and jitter in almost half of the neurons. In 3/28 neurons (11 %), dopamine significantly altered the probability of bursting. The heterogeneous effects of dopamine observed in the IC of awake mice were similar to effects observed in other brain areas. Our findings indicate that dopamine differentially modulates neural activity in the IC and thus may play an important role in auditory processing.

The effects of temperature on the stability of a neuronal oscillator

The crab Cancer borealis undergoes large daily fluctuations in environmental temperature (8-24°C) and must maintain appropriate neural function in the face of this perturbation. In the pyloric circuit of the crab stomatogastric ganglion, we pharmacologically isolated the pacemaker kernel (the AB and PD neurons) and characterized its behavior in response to temperature ramps from 7°C to 31°C. For moderate temperatures, the pacemaker displayed a frequency-temperature curve statistically indistinguishable from that of the intact circuit, and like the intact circuit maintained a constant duty cycle. At high temperatures (above 23°C), a variety of different behaviors were seen: in some preparations the pacemaker increased in frequency, in some it slowed, and in many preparations the pacemaker stopped oscillating ("crashed"). Furthermore, these crashes seemed to fall into two qualitatively different classes. Additionally, the animal-to-animal variability in frequency increased at high temperatures. We used a series of Morris-Lecar mathematical models to gain insight into these phenomena. The biophysical components of the final model have temperature sensitivities similar to those found in nature, and can crash via two qualitatively different mechanisms that resemble those observed experimentally. The crash type is determined by the precise parameters of the model at the reference temperature, 11°C, which could explain why some preparations seem to crash in one way and some in another. Furthermore, even models with very similar behavior at the reference temperature diverge greatly at high temperatures, resembling the experimental observations.

Spontaneous excitation patterns computed for axons with injury-like impairments of sodium channels and Na/K pumps

In injured neurons, “leaky” voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na⁺-loading and “Nav-CLS”, i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted I_Na-window. A recent computation study revealed that CLS-based I_Na-window left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic “smeared” injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For “mild CLS injury”, a prominent feature is slow pump/leak-mediated E_Ion oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist “device” could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.

Nerve cells damaged by trauma, stroke, epilepsy, inflammatory conditions etc, have chronically leaky sodium channels that eventually kill. The usual job of sodium channels is to make brief voltage signals –action potentials– for long distance propagation. After sodium channels open to generate action potentials, sodium pumps work harder to re-establish the intracellular/extracellular sodium imbalance that is, literally, the neuron's battery for firing action potentials. Wherever tissue damage renders membranes overly fluid, we hypothesize, sodium channels become chronically leaky. Our experimental findings justify this. In fluidized membranes, sodium channel voltage sensors respond too easily, letting channels spend too much time open. Channels leak, pumps respond. By mathematical modeling, we show that in damaged channel-rich membranes the continual pump/leak counterplay would trigger the kinds of bizarre intermittent action potential bursts typical of injured neurons. Arising ectopically from injury regions, such neuropathic firing is unrelated to events in the external world. Drugs that can silence these deleterious electrical barrages without blocking healthy action potentials are needed. If fluidized membranes house the problematic leaky sodium channels, then drug side effects could be diminished by using drugs that accumulate most avidly into fluidized membranes, and that bind their targets with highest affinity there.

Functional properties and cell type specific distribution of I(h) channels in leech neurons

The hyperpolarisation-activated cation current (I(h)) has been described in many vertebrate and invertebrate species and cell types. In neurons, I(h) is involved in rhythmogenesis, membrane potential stabilisation and many other functions. In this work, we investigate the distribution and functional properties of I(h) in identified leech neurons of intact segmental ganglia. We found I(h) in the mechanosensory touch (T), pressure (P) and noxious (N) neurons, as well as in Retzius neurons. The current displayed its largest amplitude in P neurons and we investigated its biophysical and pharmacological properties in these cells. I(h) was half-maximally activated at -65 mV and fully activated at -100 mV. The current mutually depended on both Na(+) and K(+) with a permeability ratio p(Na)/p(K) of ∼0.21. The reversal potential was approximately -35 mV. The time course of activation could be approximated by a single time constant of ∼370 ms at -60 mV, but required two time constants at -80 mV of ∼80 and ∼560 ms. The current was half-maximally blocked by 0.3 mmol l(-1) Cs(+) but was insensitive to the bradycardic agent ZD7288. The physiological function of this channel could be a subtle alteration of the firing behaviour of mechanosensory neurons as well as a stabilisation of the resting membrane potential.

Low-threshold calcium currents contribute to locomotor-like activity in neonatal mice

In this study, we examined the contribution of a low-threshold calcium current [I(Ca(T))] to locomotor-related activity in the neonatal mouse. Specifically, the role of I(Ca(T)) was studied during chemically induced, locomotor-like activity in the isolated whole cord and in a genetically distinct population of ventromedial spinal interneurons marked by the homeobox gene Hb9. In isolated whole spinal cords, cycle frequency was decreased in the presence of low-threshold calcium channel blockers, which suggests a role for I(Ca(T)) in the network that produces rhythmic, locomotor-like activity. Additionally, we used Hb9 interneurons as a model to study the cellular responses to application of low-threshold calcium channel blockers. In transverse slice preparations from transgenic Hb9::enhanced green fluorescent protein neonatal mice, N-methyl-d-aspartate-induced membrane potential oscillations in identified Hb9 interneurons also slowed in frequency with application of nickel when fast, spike-mediated, synaptic transmission was blocked with TTX. Voltage-clamp and immunolabeling experiments confirmed expression of I(Ca(T)) and channels, respectively, in Hb9 interneurons located in the ventromedial spinal cord. Taken together, these results provide support that T-type calcium currents play an important role in network-wide rhythm generation during chemically evoked, fictive locomotor activity.

Recovery of rhythmic activity in a central pattern generator: analysis of the role of neuromodulator and activity-dependent mechanisms

The pyloric network of decapods crustaceans can undergo dramatic rhythmic activity changes. Under normal conditions the network generates low frequency rhythmic activity that depends obligatorily on the presence of neuromodulatory input from the central nervous system. When this input is removed (decentralization) the rhythmic activity ceases. In the continued absence of this input, periodic activity resumes after a few hours in the form of episodic bursting across the entire network that later turns into stable rhythmic activity that is nearly indistinguishable from control (recovery). It has been proposed that an activity-dependent modification of ionic conductance levels in the pyloric pacemaker neuron drives the process of recovery of activity. Previous modeling attempts have captured some aspects of the temporal changes observed experimentally, but key features could not be reproduced. Here we examined a model in which slow activity-dependent regulation of ionic conductances and slower neuromodulator-dependent regulation of intracellular Ca(2+) concentration reproduce all the temporal features of this recovery. Key aspects of these two regulatory mechanisms are their independence and their different kinetics. We also examined the role of variability (noise) in the activity-dependent regulation pathway and observe that it can help to reduce unrealistic constraints that were otherwise required on the neuromodulator-dependent pathway. We conclude that small variations in intracellular Ca(2+) concentration, a Ca(2+) uptake regulation mechanism that is directly targeted by neuromodulator-activated signaling pathways, and variability in the Ca(2+) concentration sensing signaling pathway can account for the observed changes in neuronal activity. Our conclusions are all amenable to experimental analysis.

Variability, compensation, and modulation in neurons and circuits

I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains.

A hyperpolarization-activated inward current alters swim frequency of the pteropod mollusk Clione limacina

The pteropod mollusk, Clione limacina, exhibits behaviorally relevant swim speed changes that occur within the context of the animal's ecology. Modulation of C. limacina swimming speed involves changes that occur at the network and cellular levels. Intracellular recordings from interneurons of the swim central pattern generator show the presence of a sag potential that is indicative of the hyperpolarization-activated inward current (I(h)). Here we provide evidence that I(h) in primary swim interneurons plays a role in C. limacina swimming speed control and may be a modulatory target. Recordings from central pattern generator swim interneurons show that hyperpolarizing current injection produces a sag potential that lasts for the duration of the hyperpolarization, a characteristic of cells possessing I(h). Following the hyperpolarizing current injection, swim interneurons also exhibit postinhibitory rebound (PIR). Serotonin enhances the sag potential of C. limacina swim interneurons while the I(h) blocker, ZD7288, reduces the sag potential. Furthermore, a negative correlation was found between the amplitude of the sag potential and latency to PIR. Because latency to PIR was previously shown to influence swimming speed, we hypothesize that I(h) has an effect on swimming speed. The I(h) blocker, ZD7288, suppresses swimming in C. limacina and inhibits serotonin-induced acceleration, evidence that supports our hypothesis.

Pacemaker neuron and network oscillations depend on a neuromodulator-regulated linear current

Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current I_MI, which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of I_MI for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs.

Modulation of stomatogastric rhythms

Neuromodulation by peptides and amines is a primary source of plasticity in the nervous system as it adapts the animal to an ever-changing environment. The crustacean stomatogastric nervous system is one of the premier systems to study neuromodulation and its effects on motor pattern generation at the cellular level. It contains the extensively modulated central pattern generators that drive the gastric mill (chewing) and pyloric (food filtering) rhythms. Neuromodulators affect all stages of neuronal processing in this system, from membrane currents and synaptic transmission in network neurons to the properties of the effector muscles. The ease with which distinct neurons are identified and their activity is recorded in this system has provided considerable insight into the mechanisms by which neuromodulators affect their target cells and modulatory neuron function. Recent evidence suggests that neuromodulators are involved in homeostatic processes and that the modulatory system itself is under modulatory control, a fascinating topic whose surface has been barely scratched. Future challenges include exploring the behavioral conditions under which these systems are activated and how their effects are regulated.

How does maintenance of network activity depend on endogenous dynamics of isolated neurons?

Robust activity of some networks, such as central pattern generators, suggests the existence of physiological mechanisms that maintain the most important characteristics, for example, the period and spike frequency of the pattern. Whatever these mechanisms are, they change the appropriate model parameters to or along the isomanifolds on which the characteristics of the pattern are constant, while their sensitivities to parameters may be different. Setting synaptic connections to zero at the points of isomanifolds allows for dissecting the maintenance mechanisms into components involving synaptic transmission and components involving intrinsic currents. The physiological meaning of the intrinsic current changes might be revealed by analysis of their impact on endogenous neuronal dynamics. Here, we sought answers to two questions: (1) Do parameter variations in insensitive directions (along isomanifolds) change endogenous dynamics of the network neurons? (2) Do sensitive and insensitive directions for network pattern characteristics depend on endogenous dynamics of the network neurons? We considered a leech heartbeat half-center oscillator model network and analyzed isomanifolds on which the burst period or spike frequency of the model, or both, are constant. Based on our analysis, we hypothesize that the dependence on endogenous dynamics of the isolated neurons is the stronger the more characteristics of the pattern have to be maintained. We also found that in general, the network was more flexible when it consisted of endogenously tonically spiking rather than bursting or silent neurons. Finally, we discuss the physiological implications of our findings.

Reliable neuromodulation from circuits with variable underlying structure

Recent work argues that similar network performance can result from highly variable sets of network parameters, raising the question of whether neuromodulation can be reliable across individuals with networks with different sets of synaptic strengths and intrinsic membrane conductances. To address this question, we used the dynamic clamp to construct 2-cell reciprocally inhibitory networks from gastric mill (GM) neurons of the crab stomatogastric ganglion. When the strength of the artificial inhibitory synapses (g(syn)) and the conductance of an artificial I(h) (g(h)) were varied with the dynamic clamp, a variety of network behaviors resulted, including regions of stable alternating bursting. Maps of network output as a function of g(syn) and g(h) were constructed in normal saline and again in the presence of serotonin or oxotremorine. Both serotonin and oxotremorine depolarize and excite isolated individual GM neurons, but by different cellular mechanisms. Serotonin and oxotremorine each increased the size of the parameter regions that supported alternating bursting, and, on average, increased burst frequency. Nonetheless, in both cases some parameter sets within the sample space deviated from the mean population response and decreased in frequency. These data provide insight into why pharmacological treatments that work in most individuals can generate anomalous actions in a few individuals, and they have implications for understanding the evolution of nervous systems.

Hemodynamics in the leech: blood flow in two hearts switching between two constriction patterns

Two tubular, segmented hearts propel blood through the closed circulatory system of the medicinal leech and switch every 20-40 beats between two constriction patterns. We showed recently that within one heartbeat cycle, heart segments on one side constrict peristaltically rear-to-front (;peristaltic heart'), followed by nearly synchronous front-to-rear constrictions in the contralateral heart segments (;synchronous heart'). Using optical recordings from intact leeches, we now characterize the hemodynamic properties of the cardiac cycle of individual heart segments in different regions to ask whether the reversal of constrictions affects flow into, out of, and along the hearts. We measured total vessel capacity in corrosion casts and blood volume in individual heart segments of dissected leeches. We show that the peristaltic heart provides the propulsive force for forward and rearward flow and supplies the peripheral circulation through segmental efferent vessels. In comparison, the synchronous heart pumps less blood, most of which enters the segmental circulation. The heart sphincter, located in the posterior section of each heart segment, directs blood flow differently in the two modes. In the peristaltic heart, the sphincter prevents backflow and promotes longitudinal, forward flow while in the synchronous heart the sphincter restricts longitudinal, rearward flow and instead promotes flow into the segmental circulation. Blood is shunted via the contractile latero-dorsal arches from the dorsal intestinal vessel into the peristaltic heart in posterior segments 14 to 18. Switching between the two constriction patterns provides nutrient-rich blood to the vascular beds on both sides.

Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters

In this study, we developed a general description of parameter combinations for which specified characteristics of neuronal or network activity are constant. Our approach is based on the implicit function theorem and is applicable to activity characteristics that smoothly depend on parameters. Such smoothness is often intrinsic to neuronal systems when they are in stable functional states. The conclusions about how parameters compensate each other, developed in this study, can thus be used even without regard to the specific mathematical model describing a particular neuron or neuronal network. We showed that near a generic point in the parameter space there are infinitely many other points, or parameter combinations, for which specified characteristics of activity are the same as in the original point. These parameter combinations form a smooth manifold. This manifold can be extended as long as the gradients of characteristics are defined and independent. All possible variations of parameters compensating each other are simply all possible charts of the same manifold. The number of compensating parameters (but not parameters themselves) is fixed and equal to the number of the independent characteristics maintained. The algorithm that we developed shows how to find compensatory functional dependencies between parameters numerically. Our method can be used in the analysis of the homeostatic regulation, neuronal database search, model tuning and other applications.

A central pattern generator producing alternative outputs: pattern, strength, and dynamics of premotor synaptic input to leech heart motor neurons

The central pattern generator (CPG) for heartbeat in medicinal leeches consists of seven identified pairs of segmental heart interneurons and one unidentified pair. Four of the identified pairs and the unidentified pair of interneurons make inhibitory synaptic connections with segmental heart motor neurons. The CPG produces a side-to-side asymmetric pattern of intersegmental coordination among ipsilateral premotor interneurons corresponding to a similarly asymmetric fictive motor pattern in heart motor neurons, and asymmetric constriction pattern of the two tubular hearts, synchronous and peristaltic. Using extracellular recordings from premotor interneurons and voltage-clamp recordings of ipsilateral segmental motor neurons in 69 isolated nerve cords, we assessed the strength and dynamics of premotor inhibitory synaptic output onto the entire ensemble of heart motor neurons and the associated conduction delays in both coordination modes. We conclude that premotor interneurons establish a stereotypical pattern of intersegmental synaptic connectivity, strengths, and dynamics that is invariant across coordination modes, despite wide variations among preparations. These data coupled with a previous description of the temporal pattern of premotor interneuron activity and relative phasing of motor neuron activity in the two coordination modes enable a direct assessment of how premotor interneurons through their temporal pattern of activity and their spatial pattern of synaptic connectivity, strengths, and dynamics coordinate segmental motor neurons into a functional pattern of activity.

Inhibition of Na+/K+ ATPase potentiates synaptic transmission in tactile sensory neurons of the leech

Increasing evidence indicates that modulation of Na(+)/K(+) ATPase activity is involved in forms of neuronal and synaptic plasticity. In tactile (T) neurons of the leech Hirudo medicinalis, Na(+)/K(+) ATPase is the main determinant of the afterhyperpolarization (AHP), which characterizes the firing of these mechanosensory neurons. Previously, it has been reported that cAMP (3',5'-cyclic adenosine monophosphate), which mediates the effects of serotonin (5HT) in some forms of learning in the leech, negatively modulates Na(+)/K(+) ATPase activity, thereby reducing the AHP amplitude in T neurons. Here, we show that a transient inhibition of Na(+)/K(+) ATPase can affect the synaptic connection between two ipsilateral T neurons. Bath application of 10 nm dihydroouabain (DHO), an ouabain analogue, causes an increase in the amplitude of the synaptic potential (SP) recorded in the postsynaptic element when a test stimulus is applied in the presynaptic neuron. Iontophoretic injection of cAMP into the presynaptic T neuron also produces an increase of SP. Simulations carried out by using a computational model of the T neuron suggest that a reduction of the pump rate and a consequent depression of the AHP might facilitate the conduction of action potentials to the synaptic terminals. Moreover, nearly intact leeches injected with 10 nm DHO respond with a swimming episode more quickly to an electrical stimulation, which selectively activates T neurons exhibiting sensitization of swimming induction. Collectively, our results show that inhibition of Na(+)/K(+) ATPase is critical for short-term plasticity.

Postactivation inhibition of spontaneously active neurosecretory neurons in the medicinal leech

Spontaneously active neurosecretory neurons in vertebrate and invertebrate nervous systems share similarities in firing frequencies, spike shapes, inhibition by the transmitters they themselves release and postactivation inhibition, an intensity-dependent period of suppressed spontaneous generation of action potentials following phases of high-frequency activity. High-frequency activation of spontaneously active serotonin-containing Retzius cells in isolated ganglia of the leech Hirudo medicinalis induced prolonged membrane hyperpolarisations causing periods of postactivation inhibition of up to 33 s. The duration of the inhibitory periods was directly related to both the number and rate of spikes during activation and was inversely proportional to a cell's spontaneous firing frequency. The periods of postactivation inhibition remained unaffected by both serotonin depletion through repeated injections of 5,7-dihydroxytryptamine and suppressing the afterhyperpolarisation following each action potential with tetraethylammonium (TEA), iberiotoxin or charybdotoxin, suggesting that neither autoinhibition by synaptic release of serotonin nor calcium-activated potassium channels contribute to the underlying mechanism. In contrast, the postactivation inhibitory period was significantly affected both by differential electrical stimulation of the same Retzius cells via microelectrodes filled with molar concentrations of either Na(+)-acetate or K(+)-acetate, and by partial inhibition of Na(+)/K(+)-ATPase with ouabain. Thus, postactivation inhibition in Retzius cells results from prolonged hyperpolarising activity of Na(+)/K(+)-ATPase stimulated by the accumulation of cytosolic Na(+ )during phases of high-frequency spike activity.

Neuromodulation of central pattern generators in invertebrates and vertebrates

Central pattern generators are subject to extensive modulation that generates flexibility in the rhythmic outputs of these neural networks. The effects of neuromodulators interact with one another, and modulatory neurons are themselves often subject to modulation, enabling both higher order control and indirect interactions among central pattern generators. In addition, modulators often directly mediate the interactions between functionally related central pattern generators. In systems such as the vertebrate respiratory central pattern generator, multiple pacemaker types interact to produce rhythmic output. Modulators can then alter the relative contributions of the different pacemakers, leading to substantial changes in motor output and hence to different behaviors. Surprisingly, substantial changes in some aspects of the circuitry of a central pattern generator, such as a several-fold increase in synaptic strength, can sometimes have little effect on the output of the CPG, whereas other changes have profound effects.

Variability, compensation and homeostasis in neuron and network function

Neurons in most animals live a very long time relative to the half-lives of all of the proteins that govern excitability and synaptic transmission. Consequently, homeostatic mechanisms are necessary to ensure stable neuronal and network function over an animal's lifetime. To understand how these homeostatic mechanisms might function, it is crucial to understand how tightly regulated synaptic and intrinsic properties must be for adequate network performance, and the extent to which compensatory mechanisms allow for multiple solutions to the production of similar behaviour. Here, we use examples from theoretical and experimental studies of invertebrates and vertebrates to explore several issues relevant to understanding the precision of tuning of synaptic and intrinsic currents for the operation of functional neuronal circuits.

Creation and reduction of a morphologically detailed model of a leech heart interneuron

Conductance-based neuron models aid in understanding the role intrinsic and synaptic currents play in producing neuronal activity. Incorporating morphological detail into a model allows for additional analysis of nonhomogeneous distributions of active and synaptic conductances, as well as spatial segregation of electrical events. We developed a morphologically detailed "Full Model" of a leech heart interneuron that replicates reasonably well intracellular recordings from these interneurons. However, it constitutes hundreds of compartments, each increasing parameter space and simulation time. To reduce the number of compartments of the Full Model, while preserving conductance densities and distributions, its compartments were grouped into functional groups that each share identical conductance densities. Each functional group was sequentially reduced to one or two compartments, preserving surface area, conductance densities, and its contribution to input resistance. As a result, the input resistance and membrane time constant were preserved. The axial resistances of several compartments were rescaled to match the amplitude of synaptic currents and low-threshold calcium currents and the shape of action potentials to those in the Full Model. This reduced model, with intrinsic conductances, matched the activity of the Full Model for a variety of simulated current-clamp and voltage-clamp data. Because surface area and conductance distribution of the functional groups of the Full Model were maintained, parameter changes introduced into the reduced model can be directly translated to the Full Model. Thus our computationally efficient reduced morphology model can be used as a tool for exploring the parameter space of the Full Model and in network simulations.

Endogenous and half-center bursting in morphologically inspired models of leech heart interneurons

Based on a detailed morphology "Full Model" of a leech heart interneuron, we previously developed a computationally efficient, morphologically inspired "Reduced Model" to expedite tuning the model to produce endogenous bursting and alternating bursting when configured as a half-center oscillator (paired with reciprocally inhibitory synapses). To find conductance density distributions that produce endogenous bursting, we implemented a genetic algorithm automated parameter search. With multiple searches, we found eight parameter sets that produced endogenous bursting in the Reduced Model. When these parameter sets were applied to the Full Model, all produced endogenous bursting, although when the simulation time was extended from 80 to 300 s, only four parameter sets produced sustained bursting in the Reduced Models. All parameter sets produced alternating half-center bursting in the Reduced and Full Models throughout the entire 300 s. When conductance amplitudes were systematically varied for each of the four sustained burster sets, the effects on bursting activity differed, both for the same parameter set in the Reduced and Full Models and for different parameter sets with the same level of morphological detail. This implies that morphological detail can affect burst activity and that these parameter sets may represent different mechanisms for burst generation and/or regulation. We also tested the models with parameter variations that correspond to experimental manipulations. We conclude that, whereas similar output can be achieved with multiple different parameter sets, perturbations such as conductance variations can highlight differences. Additionally, this work demonstrates both the utility and limitations of using simplified models to represent more morphologically accurate models.